The ratio of number of one-dollar coins to the number of fifty-cent coins in a box was 3:4. Six one-dollar coins were removed and some fifty-cent coins if the same amount were added. The ratio of the number of one-dollar coins to the number of fifty-cent coins to the number of fifty-cent then became 1:3. What was the total amount of money in the box?
(3x-6)/(4x+6)=1/3
To solve this problem, we can set up and solve the equation based on the given information.
Let's start by setting up the equation based on the initial ratio of the coins:
(3x - 6) / (4x) = 3 / 4
Now let's solve for x by cross-multiplying:
4(3x - 6) = 3(4x)
12x - 24 = 12x
Since we get the same term on both sides of the equation, we can deduce that x cancels out, which means that the equation doesn't have a unique solution. This implies that there was insufficient information given in the question.
Therefore, we cannot determine the total amount of money in the box with the available information.
To find the total amount of money in the box, we first need to determine the values for x in the given equation.
The ratio of the number of one-dollar coins to the number of fifty-cent coins initially is 3:4, which can be represented as (3x-6)/(4x).
After removing six one-dollar coins and adding an equal number of fifty-cent coins, the new ratio becomes 1:3, which is represented as (3x-6)/(4x+6).
Now, we have the equation: (3x-6)/(4x+6) = 1/3.
To solve the equation, we can cross-multiply: 3(3x-6) = (4x+6).
Expanding the equation gives us: 9x - 18 = 4x + 6.
Next, we can solve for x by isolating the variable terms: 9x - 4x = 6 + 18.
Combining like terms, we get: 5x = 24.
Finally, dividing both sides of the equation by 5 gives us: x = 24/5 = 4.8.
Now that we have the value for x, we can find the original number of one-dollar coins and fifty-cent coins.
Substituting x = 4.8 into the original ratio (3x-6)/(4x), we get (3 * 4.8 - 6) / (4 * 4.8) = 10/16.
Simplifying the fraction, we find that the original ratio was 5/8.
Now, we can calculate the total amount of money in the box.
Let's assume each one-dollar coin is worth $1 and each fifty-cent coin is worth $0.50.
The initial value of the one-dollar coins was 5 * $1 = $5.
The initial value of the fifty-cent coins was 8 * $0.50 = $4.
Therefore, the total amount of money in the box initially was $5 + $4 = $9.
(3x-6)/(4x+12) = 1/3
it takes 12 fifty-cent coins to be "the same amount" as six dollar coins
number of $1 coins --- 3x
number of half-dollars --- 4x
Your second sentence does not make any sense to me
taking your equation ...
cross-multiply
9x - 18 = 4x+6
5x = 24
x = ???? , x must be a whole number
Fix your second sentence.